# What is the second row of entries for the system determinant? 2x - y = 5 , x + 3y = 7

0, 3

1, 3

3, 7

**Solution: **

The given set of equations are 2x - y = 5 and x + 3y = 7

The rows of the determinant are based on the equations

The first equation will describe the first row of the determinant and the second equation will describe the second row of the equation

Therefore, the second row of the determinant will be the value of x and y. i.e., 1, 3.

2d square matrix is written as:

\(\left[\begin{array}{ll}2 & -1 \\1 & 3\end{array}\right]\)

Also, the value of the 2D determinant can be evaluated using the determinant formula:

|C| = \(\left|\begin{array}{ll}2 & -1 \\1 & 3\end{array}\right|\)

|C| = x\(_1\)y\(_2\)_{ }- y\(_1\)x\(_2\)

⇒ 2(3) - (-1)(1)

⇒ 6 + 1

⇒ 7

## What is the second row of entries for the system determinant? 2x - y = 5 , x + 3y = 7

**Summary: **

The second row of the determinant for the given set of equations 2x - y = 5 and x + 3y = 7 is given by 1, 3 and the value of the determinant is 7.